Piecewise Loglinear Estimation of Efficient Production Surfaces

Linear programming formulations for piecewise loglinear estimation of efficient production surfaces are derived from a set of basic properties postulated for the underlying production possibility sets. Unlike the piecewise linear model of Banker, Charnes, and Cooper (Banker R. D., A. Charnes, W. W. Cooper. 1984. Models for the estimation of technical and scale inefficiencies in data envelopment analysis. Management Sci. 30 (September) 1078--1092.), this approach permits the identification of increasing marginal products, and estimation of the classical S-shaped production functions. Methods are also provided for estimating technical inefficiencies and other production characteristics, such as rates of substitution and transformation, marginal products, returns to scale and most productive scale sizes on the basis of observed production data. The results of a simulation study are reported to illustrate the usefulness of this estimation method in empirical applications when there are a priori reasons to expect increasing marginal products in some regions of the production function. A modified model is provided to extend this analysis to the situation of non-competing outputs addressed by the bi-extremal model of Banker, Charnes, Cooper, and Schinnar (Banker R. D., A. Charnes, W. W. Cooper, A. Schinnar. 1981. A bi-extremal principle for frontier estimation and efficiency evaluation. Management Sci. 27 (December) 1370--1382.).